On groups with
many abelian-by-finite quotients

Oksana Turash

Soluble $\operatorname{JNAF}$-$p$-groups and periodic soluble $\operatorname{JNAF}$-groups with abelian Fitting subgroup are characterized. It is proved that any locally nilpotent torsion-free $\operatorname{JNAF}$-group either has the trivial Fitting subgroup or is a nilpotent group with locally cyclic centre. Nilpotent torsion-free $\operatorname{JNAF}$-groups with divisible centre are also characterized.

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3. Wilson J.S. Groups with every proper quotient finite// Math. Proc. Cambridge Phil. Soc.– 1971 V. 69 p. 373–391

4. Robinson D.J.S., Wilson J.S. Soluble groups with many polycyclic quotients// Proc. London. Math. Soc.–1984 V.3 N.48 p. 193–229

5. Franciosi S, de Giovanni F. Soluble groups with many Černikov quotients// Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.– 1985 V. 79 N. 8 p. 19–24

6. Robinson D.J.S., Zhirang Zhang Groups whose proper quotients have finite derived subgroups// J. Algebra– 1988 V.118 p. 346–368

7. S. Franciosi, F. Giovanni, L.A. Kurdachenko Groups whose proper quotients are $FC$-groups// Università degli di Napoli, preprint N. 64-- 1995, Ñ.157.

8. Курдаченко Л.А., Пылаев В.В. О группах с минимаксными фактор-группами. Укр. мат. ж., 42 (1990), №5, 620–625.

9. С.Н. Черников. Группы с заданными свойствами системы подгрупп. М.: Наука, 1980.

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11. G .Baumslag Wreath products and $p$-groups// Proc. Cambridge Phil. Soc.-- 1959 V. 55 p. 224--231

12. A. Betten Hinreichende Kriterien fur die Hyperzentralität einer Gruppen// Arch. Math.– 1969 V.20 p.471–480

13. Franciosi S., de Giovanni F. On torsion groups with nilpotent automorphis groups// Commut. Algebra– 1986 V. 14 p. 1909–1935

14. D.J.S. Robinson Splitting theorem for infinite groups// Symposia Math.– 1976 V. 17 p. 441–470

15. D.J.S. Robinson Finiteness conditions and generalized soluble groups,addr Berlin, Springer

	On groups with many abelian-by-finite quotients
Author	Oksana Turash
Abstract	Soluble $\operatorname{JNAF}$-$p$-groups and periodic soluble $\operatorname{JNAF}$-groups with abelian Fitting subgroup are characterized. It is proved that any locally nilpotent torsion-free $\operatorname{JNAF}$-group either has the trivial Fitting subgroup or is a nilpotent group with locally cyclic centre. Nilpotent torsion-free $\operatorname{JNAF}$-groups with divisible centre are also characterized.
Keywords	soluble JNAF-groups, periodic groups, abelian Fitting subgroup, locally nilpotent groups, locally cyclic centre, divisible centre
DOI	doi:10.30970/ms.8.1.15-20
Reference	1. Newman M.F. On a class of metabelian groups// Proc. London Math. Soc. – 1960 V.3 N.10 p. 354–364 2. Newman M.F. On a class of nilpotent groups// Proc. London Math. Soc. – 1960 V.3 N.10 p. 365–375 3. Wilson J.S. Groups with every proper quotient finite// Math. Proc. Cambridge Phil. Soc.– 1971 V. 69 p. 373–391 4. Robinson D.J.S., Wilson J.S. Soluble groups with many polycyclic quotients// Proc. London. Math. Soc.–1984 V.3 N.48 p. 193–229 5. Franciosi S, de Giovanni F. Soluble groups with many Černikov quotients// Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.– 1985 V. 79 N. 8 p. 19–24 6. Robinson D.J.S., Zhirang Zhang Groups whose proper quotients have finite derived subgroups// J. Algebra– 1988 V.118 p. 346–368 7. S. Franciosi, F. Giovanni, L.A. Kurdachenko Groups whose proper quotients are $FC$-groups// Università degli di Napoli, preprint N. 64-- 1995, Ñ.157. 8. Курдаченко Л.А., Пылаев В.В. О группах с минимаксными фактор-группами. Укр. мат. ж., 42 (1990), №5, 620–625. 9. С.Н. Черников. Группы с заданными свойствами системы подгрупп. М.: Наука, 1980. 10. D.J.S. Robinson A course in the theory of group, Springer,addr New York e.a.– 1982 11. G .Baumslag Wreath products and $p$-groups// Proc. Cambridge Phil. Soc.-- 1959 V. 55 p. 224--231 12. A. Betten Hinreichende Kriterien fur die Hyperzentralität einer Gruppen// Arch. Math.– 1969 V.20 p.471–480 13. Franciosi S., de Giovanni F. On torsion groups with nilpotent automorphis groups// Commut. Algebra– 1986 V. 14 p. 1909–1935 14. D.J.S. Robinson Splitting theorem for infinite groups// Symposia Math.– 1976 V. 17 p. 441–470 15. D.J.S. Robinson Finiteness conditions and generalized soluble groups,addr Berlin, Springer
Pages	15-20
Volume	8
Issue	1
Year	1997
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

On groups with many abelian-by-finite quotients